LMFDB - Embedded newform 6018.2.a.y.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6018,2,Mod(1,6018)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6018, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6018 = 2 \cdot 3 \cdot 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6018.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.0539719364$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 33x^{8} + 53x^{7} + 356x^{6} - 433x^{5} - 1296x^{4} + 1135x^{3} + 930x^{2} - 186x - 104 $ x^10 - 2x^9 - 33x^8 + 53x^7 + 356x^6 - 433x^5 - 1296x^4 + 1135x^3 + 930x^2 - 186*x - 104
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-2.34533$ of defining polynomial
Character	$\chi$	$=$	6018.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.34533 q^{5} -1.00000 q^{6} -0.244087 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.34533 q^{5} -1.00000 q^{6} -0.244087 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.34533 q^{10} -4.39089 q^{11} +1.00000 q^{12} -2.05270 q^{13} +0.244087 q^{14} +2.34533 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} -3.20608 q^{19} +2.34533 q^{20} -0.244087 q^{21} +4.39089 q^{22} +6.26711 q^{23} -1.00000 q^{24} +0.500551 q^{25} +2.05270 q^{26} +1.00000 q^{27} -0.244087 q^{28} -3.55033 q^{29} -2.34533 q^{30} -4.26717 q^{31} -1.00000 q^{32} -4.39089 q^{33} +1.00000 q^{34} -0.572465 q^{35} +1.00000 q^{36} +2.99469 q^{37} +3.20608 q^{38} -2.05270 q^{39} -2.34533 q^{40} -3.76878 q^{41} +0.244087 q^{42} +5.24504 q^{43} -4.39089 q^{44} +2.34533 q^{45} -6.26711 q^{46} -2.97697 q^{47} +1.00000 q^{48} -6.94042 q^{49} -0.500551 q^{50} -1.00000 q^{51} -2.05270 q^{52} +2.49863 q^{53} -1.00000 q^{54} -10.2981 q^{55} +0.244087 q^{56} -3.20608 q^{57} +3.55033 q^{58} +1.00000 q^{59} +2.34533 q^{60} +7.35455 q^{61} +4.26717 q^{62} -0.244087 q^{63} +1.00000 q^{64} -4.81424 q^{65} +4.39089 q^{66} +8.88079 q^{67} -1.00000 q^{68} +6.26711 q^{69} +0.572465 q^{70} +6.40140 q^{71} -1.00000 q^{72} -2.18336 q^{73} -2.99469 q^{74} +0.500551 q^{75} -3.20608 q^{76} +1.07176 q^{77} +2.05270 q^{78} +0.771377 q^{79} +2.34533 q^{80} +1.00000 q^{81} +3.76878 q^{82} -16.0036 q^{83} -0.244087 q^{84} -2.34533 q^{85} -5.24504 q^{86} -3.55033 q^{87} +4.39089 q^{88} -5.53517 q^{89} -2.34533 q^{90} +0.501037 q^{91} +6.26711 q^{92} -4.26717 q^{93} +2.97697 q^{94} -7.51929 q^{95} -1.00000 q^{96} -5.16986 q^{97} +6.94042 q^{98} -4.39089 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} + 10 q^{3} + 10 q^{4} - 2 q^{5} - 10 q^{6} - 6 q^{7} - 10 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 + 10 * q^3 + 10 * q^4 - 2 * q^5 - 10 * q^6 - 6 * q^7 - 10 * q^8 + 10 * q^9	\( 10 q - 10 q^{2} + 10 q^{3} + 10 q^{4} - 2 q^{5} - 10 q^{6} - 6 q^{7} - 10 q^{8} + 10 q^{9} + 2 q^{10} - 3 q^{11} + 10 q^{12} - 10 q^{13} + 6 q^{14} - 2 q^{15} + 10 q^{16} - 10 q^{17} - 10 q^{18} + 8 q^{19} - 2 q^{20} - 6 q^{21} + 3 q^{22} - 9 q^{23} - 10 q^{24} + 20 q^{25} + 10 q^{26} + 10 q^{27} - 6 q^{28} - 24 q^{29} + 2 q^{30} - 7 q^{31} - 10 q^{32} - 3 q^{33} + 10 q^{34} - 22 q^{35} + 10 q^{36} - 4 q^{37} - 8 q^{38} - 10 q^{39} + 2 q^{40} - 9 q^{41} + 6 q^{42} - 11 q^{43} - 3 q^{44} - 2 q^{45} + 9 q^{46} - 18 q^{47} + 10 q^{48} + 6 q^{49} - 20 q^{50} - 10 q^{51} - 10 q^{52} - 9 q^{53} - 10 q^{54} + q^{55} + 6 q^{56} + 8 q^{57} + 24 q^{58} + 10 q^{59} - 2 q^{60} - 25 q^{61} + 7 q^{62} - 6 q^{63} + 10 q^{64} - 28 q^{65} + 3 q^{66} + 2 q^{67} - 10 q^{68} - 9 q^{69} + 22 q^{70} - 30 q^{71} - 10 q^{72} - 11 q^{73} + 4 q^{74} + 20 q^{75} + 8 q^{76} + 4 q^{77} + 10 q^{78} + 3 q^{79} - 2 q^{80} + 10 q^{81} + 9 q^{82} - q^{83} - 6 q^{84} + 2 q^{85} + 11 q^{86} - 24 q^{87} + 3 q^{88} - 14 q^{89} + 2 q^{90} - 13 q^{91} - 9 q^{92} - 7 q^{93} + 18 q^{94} - 35 q^{95} - 10 q^{96} - 10 q^{97} - 6 q^{98} - 3 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 + 10 * q^3 + 10 * q^4 - 2 * q^5 - 10 * q^6 - 6 * q^7 - 10 * q^8 + 10 * q^9 + 2 * q^10 - 3 * q^11 + 10 * q^12 - 10 * q^13 + 6 * q^14 - 2 * q^15 + 10 * q^16 - 10 * q^17 - 10 * q^18 + 8 * q^19 - 2 * q^20 - 6 * q^21 + 3 * q^22 - 9 * q^23 - 10 * q^24 + 20 * q^25 + 10 * q^26 + 10 * q^27 - 6 * q^28 - 24 * q^29 + 2 * q^30 - 7 * q^31 - 10 * q^32 - 3 * q^33 + 10 * q^34 - 22 * q^35 + 10 * q^36 - 4 * q^37 - 8 * q^38 - 10 * q^39 + 2 * q^40 - 9 * q^41 + 6 * q^42 - 11 * q^43 - 3 * q^44 - 2 * q^45 + 9 * q^46 - 18 * q^47 + 10 * q^48 + 6 * q^49 - 20 * q^50 - 10 * q^51 - 10 * q^52 - 9 * q^53 - 10 * q^54 + q^55 + 6 * q^56 + 8 * q^57 + 24 * q^58 + 10 * q^59 - 2 * q^60 - 25 * q^61 + 7 * q^62 - 6 * q^63 + 10 * q^64 - 28 * q^65 + 3 * q^66 + 2 * q^67 - 10 * q^68 - 9 * q^69 + 22 * q^70 - 30 * q^71 - 10 * q^72 - 11 * q^73 + 4 * q^74 + 20 * q^75 + 8 * q^76 + 4 * q^77 + 10 * q^78 + 3 * q^79 - 2 * q^80 + 10 * q^81 + 9 * q^82 - q^83 - 6 * q^84 + 2 * q^85 + 11 * q^86 - 24 * q^87 + 3 * q^88 - 14 * q^89 + 2 * q^90 - 13 * q^91 - 9 * q^92 - 7 * q^93 + 18 * q^94 - 35 * q^95 - 10 * q^96 - 10 * q^97 - 6 * q^98 - 3 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	2.34533	1.04886	0.524431	−	0.851453i	$-0.324278\pi$
$5$	2.34533	1.04886	0.524431	+	0.851453i	$0.324278\pi$
$6$	−1.00000	−0.408248
$7$	−0.244087	−0.0922564	−0.0461282	−	0.998936i	$-0.514688\pi$
$7$	−0.244087	−0.0922564	−0.0461282	+	0.998936i	$0.514688\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−2.34533	−0.741657
$11$	−4.39089	−1.32390	−0.661951	−	0.749547i	$-0.730271\pi$
$11$	−4.39089	−1.32390	−0.661951	+	0.749547i	$0.730271\pi$
$12$	1.00000	0.288675
$13$	−2.05270	−0.569315	−0.284658	−	0.958629i	$-0.591880\pi$
$13$	−2.05270	−0.569315	−0.284658	+	0.958629i	$0.591880\pi$
$14$	0.244087	0.0652351
$15$	2.34533	0.605560
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.00000	−0.235702
$19$	−3.20608	−0.735524	−0.367762	−	0.929920i	$-0.619876\pi$
$19$	−3.20608	−0.735524	−0.367762	+	0.929920i	$0.619876\pi$
$20$	2.34533	0.524431
$21$	−0.244087	−0.0532643
$22$	4.39089	0.936140
$23$	6.26711	1.30678	0.653392	−	0.757020i	$-0.273346\pi$
$23$	6.26711	1.30678	0.653392	+	0.757020i	$0.273346\pi$
$24$	−1.00000	−0.204124
$25$	0.500551	0.100110
$26$	2.05270	0.402567
$27$	1.00000	0.192450
$28$	−0.244087	−0.0461282
$29$	−3.55033	−0.659280	−0.329640	−	0.944107i	$-0.606927\pi$
$29$	−3.55033	−0.659280	−0.329640	+	0.944107i	$0.606927\pi$
$30$	−2.34533	−0.428196
$31$	−4.26717	−0.766407	−0.383203	−	0.923664i	$-0.625179\pi$
$31$	−4.26717	−0.766407	−0.383203	+	0.923664i	$0.625179\pi$
$32$	−1.00000	−0.176777
$33$	−4.39089	−0.764355
$34$	1.00000	0.171499
$35$	−0.572465	−0.0967642
$36$	1.00000	0.166667
$37$	2.99469	0.492324	0.246162	−	0.969229i	$-0.420831\pi$
$37$	2.99469	0.492324	0.246162	+	0.969229i	$0.420831\pi$
$38$	3.20608	0.520094
$39$	−2.05270	−0.328694
$40$	−2.34533	−0.370828
$41$	−3.76878	−0.588584	−0.294292	−	0.955716i	$-0.595084\pi$
$41$	−3.76878	−0.588584	−0.294292	+	0.955716i	$0.595084\pi$
$42$	0.244087	0.0376635
$43$	5.24504	0.799861	0.399930	−	0.916546i	$-0.369034\pi$
$43$	5.24504	0.799861	0.399930	+	0.916546i	$0.369034\pi$
$44$	−4.39089	−0.661951
$45$	2.34533	0.349620
$46$	−6.26711	−0.924035
$47$	−2.97697	−0.434235	−0.217118	−	0.976145i	$-0.569666\pi$
$47$	−2.97697	−0.434235	−0.217118	+	0.976145i	$0.569666\pi$
$48$	1.00000	0.144338
$49$	−6.94042	−0.991489
$50$	−0.500551	−0.0707886
$51$	−1.00000	−0.140028
$52$	−2.05270	−0.284658
$53$	2.49863	0.343213	0.171607	−	0.985166i	$-0.445104\pi$
$53$	2.49863	0.343213	0.171607	+	0.985166i	$0.445104\pi$
$54$	−1.00000	−0.136083
$55$	−10.2981	−1.38859
$56$	0.244087	0.0326176
$57$	−3.20608	−0.424655
$58$	3.55033	0.466181
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	2.34533	0.302780
$61$	7.35455	0.941653	0.470827	−	0.882226i	$-0.343956\pi$
$61$	7.35455	0.941653	0.470827	+	0.882226i	$0.343956\pi$
$62$	4.26717	0.541931
$63$	−0.244087	−0.0307521
$64$	1.00000	0.125000
$65$	−4.81424	−0.597133
$66$	4.39089	0.540481
$67$	8.88079	1.08496	0.542481	−	0.840068i	$-0.317485\pi$
$67$	8.88079	1.08496	0.542481	+	0.840068i	$0.317485\pi$
$68$	−1.00000	−0.121268
$69$	6.26711	0.754472
$70$	0.572465	0.0684226
$71$	6.40140	0.759706	0.379853	−	0.925047i	$-0.375975\pi$
$71$	6.40140	0.759706	0.379853	+	0.925047i	$0.375975\pi$
$72$	−1.00000	−0.117851
$73$	−2.18336	−0.255543	−0.127772	−	0.991804i	$-0.540782\pi$
$73$	−2.18336	−0.255543	−0.127772	+	0.991804i	$0.540782\pi$
$74$	−2.99469	−0.348125
$75$	0.500551	0.0577986
$76$	−3.20608	−0.367762
$77$	1.07176	0.122138
$78$	2.05270	0.232422
$79$	0.771377	0.0867867	0.0433934	−	0.999058i	$-0.486183\pi$
$79$	0.771377	0.0867867	0.0433934	+	0.999058i	$0.486183\pi$
$80$	2.34533	0.262215
$81$	1.00000	0.111111
$82$	3.76878	0.416192
$83$	−16.0036	−1.75662	−0.878311	−	0.478090i	$-0.841329\pi$
$83$	−16.0036	−1.75662	−0.878311	+	0.478090i	$0.841329\pi$
$84$	−0.244087	−0.0266321
$85$	−2.34533	−0.254386
$86$	−5.24504	−0.565587
$87$	−3.55033	−0.380635
$88$	4.39089	0.468070
$89$	−5.53517	−0.586726	−0.293363	−	0.956001i	$-0.594775\pi$
$89$	−5.53517	−0.586726	−0.293363	+	0.956001i	$0.594775\pi$
$90$	−2.34533	−0.247219
$91$	0.501037	0.0525230
$92$	6.26711	0.653392
$93$	−4.26717	−0.442485
$94$	2.97697	0.307051
$95$	−7.51929	−0.771463
$96$	−1.00000	−0.102062
$97$	−5.16986	−0.524920	−0.262460	−	0.964943i	$-0.584534\pi$
$97$	−5.16986	−0.524920	−0.262460	+	0.964943i	$0.584534\pi$
$98$	6.94042	0.701088
$99$	−4.39089	−0.441301
$100$	0.500551	0.0500551
$101$	−7.23403	−0.719813	−0.359907	−	0.932988i	$-0.617191\pi$
$101$	−7.23403	−0.719813	−0.359907	+	0.932988i	$0.617191\pi$
$102$	1.00000	0.0990148
$103$	−9.82845	−0.968425	−0.484213	−	0.874950i	$-0.660894\pi$
$103$	−9.82845	−0.968425	−0.484213	+	0.874950i	$0.660894\pi$
$104$	2.05270	0.201283
$105$	−0.572465	−0.0558668
$106$	−2.49863	−0.242689
$107$	−11.4090	−1.10295	−0.551474	−	0.834192i	$-0.685935\pi$
$107$	−11.4090	−1.10295	−0.551474	+	0.834192i	$0.685935\pi$
$108$	1.00000	0.0962250
$109$	−17.5802	−1.68388	−0.841939	−	0.539572i	$-0.818586\pi$
$109$	−17.5802	−1.68388	−0.841939	+	0.539572i	$0.818586\pi$
$110$	10.2981	0.981881
$111$	2.99469	0.284243
$112$	−0.244087	−0.0230641
$113$	6.87393	0.646645	0.323323	−	0.946289i	$-0.395200\pi$
$113$	6.87393	0.646645	0.323323	+	0.946289i	$0.395200\pi$
$114$	3.20608	0.300277
$115$	14.6984	1.37063
$116$	−3.55033	−0.329640
$117$	−2.05270	−0.189772
$118$	−1.00000	−0.0920575
$119$	0.244087	0.0223755
$120$	−2.34533	−0.214098
$121$	8.27989	0.752717
$122$	−7.35455	−0.665849
$123$	−3.76878	−0.339819
$124$	−4.26717	−0.383203
$125$	−10.5527	−0.943860
$126$	0.244087	0.0217450
$127$	−2.11142	−0.187358	−0.0936790	−	0.995602i	$-0.529863\pi$
$127$	−2.11142	−0.187358	−0.0936790	+	0.995602i	$0.529863\pi$
$128$	−1.00000	−0.0883883
$129$	5.24504	0.461800
$130$	4.81424	0.422237
$131$	−18.3512	−1.60335	−0.801675	−	0.597761i	$-0.796057\pi$
$131$	−18.3512	−1.60335	−0.801675	+	0.597761i	$0.796057\pi$
$132$	−4.39089	−0.382178
$133$	0.782563	0.0678568
$134$	−8.88079	−0.767184
$135$	2.34533	0.201853
$136$	1.00000	0.0857493
$137$	−15.2719	−1.30477	−0.652384	−	0.757889i	$-0.726231\pi$
$137$	−15.2719	−1.30477	−0.652384	+	0.757889i	$0.726231\pi$
$138$	−6.26711	−0.533492
$139$	−20.2337	−1.71620	−0.858100	−	0.513482i	$-0.828355\pi$
$139$	−20.2337	−1.71620	−0.858100	+	0.513482i	$0.828355\pi$
$140$	−0.572465	−0.0483821
$141$	−2.97697	−0.250706
$142$	−6.40140	−0.537193
$143$	9.01316	0.753718
$144$	1.00000	0.0833333
$145$	−8.32668	−0.691493
$146$	2.18336	0.180696
$147$	−6.94042	−0.572436
$148$	2.99469	0.246162
$149$	9.86871	0.808476	0.404238	−	0.914654i	$-0.367537\pi$
$149$	9.86871	0.808476	0.404238	+	0.914654i	$0.367537\pi$
$150$	−0.500551	−0.0408698
$151$	−8.32774	−0.677702	−0.338851	−	0.940840i	$-0.610038\pi$
$151$	−8.32774	−0.677702	−0.338851	+	0.940840i	$0.610038\pi$
$152$	3.20608	0.260047
$153$	−1.00000	−0.0808452
$154$	−1.07176	−0.0863649
$155$	−10.0079	−0.803854
$156$	−2.05270	−0.164347
$157$	0.502553	0.0401081	0.0200540	−	0.999799i	$-0.493616\pi$
$157$	0.502553	0.0401081	0.0200540	+	0.999799i	$0.493616\pi$
$158$	−0.771377	−0.0613675
$159$	2.49863	0.198154
$160$	−2.34533	−0.185414
$161$	−1.52972	−0.120559
$162$	−1.00000	−0.0785674
$163$	6.32513	0.495422	0.247711	−	0.968834i	$-0.420322\pi$
$163$	6.32513	0.495422	0.247711	+	0.968834i	$0.420322\pi$
$164$	−3.76878	−0.294292
$165$	−10.2981	−0.801703
$166$	16.0036	1.24212
$167$	9.75443	0.754821	0.377410	−	0.926046i	$-0.376815\pi$
$167$	9.75443	0.754821	0.377410	+	0.926046i	$0.376815\pi$
$168$	0.244087	0.0188318
$169$	−8.78644	−0.675880
$170$	2.34533	0.179878
$171$	−3.20608	−0.245175
$172$	5.24504	0.399930
$173$	−22.7714	−1.73127	−0.865637	−	0.500672i	$-0.833086\pi$
$173$	−22.7714	−1.73127	−0.865637	+	0.500672i	$0.833086\pi$
$174$	3.55033	0.269150
$175$	−0.122178	−0.00923580
$176$	−4.39089	−0.330976
$177$	1.00000	0.0751646
$178$	5.53517	0.414878
$179$	−15.4874	−1.15758	−0.578792	−	0.815475i	$-0.696476\pi$
$179$	−15.4874	−1.15758	−0.578792	+	0.815475i	$0.696476\pi$
$180$	2.34533	0.174810
$181$	25.3733	1.88598	0.942991	−	0.332818i	$-0.108000\pi$
$181$	25.3733	1.88598	0.942991	+	0.332818i	$0.108000\pi$
$182$	−0.501037	−0.0371394
$183$	7.35455	0.543664
$184$	−6.26711	−0.462018
$185$	7.02352	0.516379
$186$	4.26717	0.312884
$187$	4.39089	0.321093
$188$	−2.97697	−0.217118
$189$	−0.244087	−0.0177548
$190$	7.51929	0.545507
$191$	−19.4985	−1.41086	−0.705429	−	0.708780i	$-0.749246\pi$
$191$	−19.4985	−1.41086	−0.705429	+	0.708780i	$0.749246\pi$
$192$	1.00000	0.0721688
$193$	2.34396	0.168722	0.0843609	−	0.996435i	$-0.473115\pi$
$193$	2.34396	0.168722	0.0843609	+	0.996435i	$0.473115\pi$
$194$	5.16986	0.371174
$195$	−4.81424	−0.344755
$196$	−6.94042	−0.495744
$197$	22.6806	1.61593	0.807963	−	0.589233i	$-0.200570\pi$
$197$	22.6806	1.61593	0.807963	+	0.589233i	$0.200570\pi$
$198$	4.39089	0.312047
$199$	9.89201	0.701226	0.350613	−	0.936520i	$-0.385973\pi$
$199$	9.89201	0.701226	0.350613	+	0.936520i	$0.385973\pi$
$200$	−0.500551	−0.0353943
$201$	8.88079	0.626403
$202$	7.23403	0.508985
$203$	0.866591	0.0608228
$204$	−1.00000	−0.0700140
$205$	−8.83900	−0.617343
$206$	9.82845	0.684780
$207$	6.26711	0.435594
$208$	−2.05270	−0.142329
$209$	14.0775	0.973762
$210$	0.572465	0.0395038
$211$	−18.3306	−1.26193	−0.630967	−	0.775810i	$-0.717342\pi$
$211$	−18.3306	−1.26193	−0.630967	+	0.775810i	$0.717342\pi$
$212$	2.49863	0.171607
$213$	6.40140	0.438616
$214$	11.4090	0.779903
$215$	12.3013	0.838943
$216$	−1.00000	−0.0680414
$217$	1.04156	0.0707059
$218$	17.5802	1.19068
$219$	−2.18336	−0.147538
$220$	−10.2981	−0.694295
$221$	2.05270	0.138079
$222$	−2.99469	−0.200990
$223$	2.97345	0.199117	0.0995585	−	0.995032i	$-0.468257\pi$
$223$	2.97345	0.199117	0.0995585	+	0.995032i	$0.468257\pi$
$224$	0.244087	0.0163088
$225$	0.500551	0.0333701
$226$	−6.87393	−0.457247
$227$	−12.2822	−0.815197	−0.407599	−	0.913161i	$-0.633634\pi$
$227$	−12.2822	−0.815197	−0.407599	+	0.913161i	$0.633634\pi$
$228$	−3.20608	−0.212328
$229$	3.89318	0.257269	0.128634	−	0.991692i	$-0.458941\pi$
$229$	3.89318	0.257269	0.128634	+	0.991692i	$0.458941\pi$
$230$	−14.6984	−0.969185
$231$	1.07176	0.0705167
$232$	3.55033	0.233091
$233$	−15.5629	−1.01956	−0.509781	−	0.860304i	$-0.670273\pi$
$233$	−15.5629	−1.01956	−0.509781	+	0.860304i	$0.670273\pi$
$234$	2.05270	0.134189
$235$	−6.98196	−0.455453
$236$	1.00000	0.0650945
$237$	0.771377	0.0501063
$238$	−0.244087	−0.0158218
$239$	19.3551	1.25198	0.625990	−	0.779831i	$-0.284695\pi$
$239$	19.3551	1.25198	0.625990	+	0.779831i	$0.284695\pi$
$240$	2.34533	0.151390
$241$	23.0940	1.48762	0.743809	−	0.668393i	$-0.233017\pi$
$241$	23.0940	1.48762	0.743809	+	0.668393i	$0.233017\pi$
$242$	−8.27989	−0.532251
$243$	1.00000	0.0641500
$244$	7.35455	0.470827
$245$	−16.2775	−1.03993
$246$	3.76878	0.240288
$247$	6.58110	0.418745
$248$	4.26717	0.270966
$249$	−16.0036	−1.01419
$250$	10.5527	0.667410
$251$	−12.0132	−0.758268	−0.379134	−	0.925342i	$-0.623778\pi$
$251$	−12.0132	−0.758268	−0.379134	+	0.925342i	$0.623778\pi$
$252$	−0.244087	−0.0153761
$253$	−27.5182	−1.73005
$254$	2.11142	0.132482
$255$	−2.34533	−0.146870
$256$	1.00000	0.0625000
$257$	23.5780	1.47075	0.735377	−	0.677658i	$-0.237005\pi$
$257$	23.5780	1.47075	0.735377	+	0.677658i	$0.237005\pi$
$258$	−5.24504	−0.326542
$259$	−0.730966	−0.0454200
$260$	−4.81424	−0.298567
$261$	−3.55033	−0.219760
$262$	18.3512	1.13374
$263$	−0.246600	−0.0152060	−0.00760302	−	0.999971i	$-0.502420\pi$
$263$	−0.246600	−0.0152060	−0.00760302	+	0.999971i	$0.502420\pi$
$264$	4.39089	0.270240
$265$	5.86010	0.359983
$266$	−0.782563	−0.0479820
$267$	−5.53517	−0.338747
$268$	8.88079	0.542481
$269$	−19.3872	−1.18206	−0.591029	−	0.806650i	$-0.701278\pi$
$269$	−19.3872	−1.18206	−0.591029	+	0.806650i	$0.701278\pi$
$270$	−2.34533	−0.142732
$271$	−27.2887	−1.65767	−0.828836	−	0.559491i	$-0.810997\pi$
$271$	−27.2887	−1.65767	−0.828836	+	0.559491i	$0.810997\pi$
$272$	−1.00000	−0.0606339
$273$	0.501037	0.0303242
$274$	15.2719	0.922610
$275$	−2.19786	−0.132536
$276$	6.26711	0.377236
$277$	7.58671	0.455841	0.227921	−	0.973680i	$-0.426807\pi$
$277$	7.58671	0.455841	0.227921	+	0.973680i	$0.426807\pi$
$278$	20.2337	1.21354
$279$	−4.26717	−0.255469
$280$	0.572465	0.0342113
$281$	−11.4719	−0.684359	−0.342179	−	0.939635i	$-0.611165\pi$
$281$	−11.4719	−0.684359	−0.342179	+	0.939635i	$0.611165\pi$
$282$	2.97697	0.177276
$283$	27.0012	1.60506	0.802529	−	0.596614i	$-0.203488\pi$
$283$	27.0012	1.60506	0.802529	+	0.596614i	$0.203488\pi$
$284$	6.40140	0.379853
$285$	−7.51929	−0.445404
$286$	−9.01316	−0.532959
$287$	0.919911	0.0543006
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	8.32668	0.488960
$291$	−5.16986	−0.303063
$292$	−2.18336	−0.127772
$293$	4.10937	0.240072	0.120036	−	0.992770i	$-0.461699\pi$
$293$	4.10937	0.240072	0.120036	+	0.992770i	$0.461699\pi$
$294$	6.94042	0.404774
$295$	2.34533	0.136550
$296$	−2.99469	−0.174063
$297$	−4.39089	−0.254785
$298$	−9.86871	−0.571679
$299$	−12.8645	−0.743972
$300$	0.500551	0.0288993
$301$	−1.28025	−0.0737923
$302$	8.32774	0.479208
$303$	−7.23403	−0.415584
$304$	−3.20608	−0.183881
$305$	17.2488	0.987664
$306$	1.00000	0.0571662
$307$	24.2877	1.38617	0.693085	−	0.720856i	$-0.256251\pi$
$307$	24.2877	1.38617	0.693085	+	0.720856i	$0.256251\pi$
$308$	1.07176	0.0610692
$309$	−9.82845	−0.559121
$310$	10.0079	0.568411
$311$	−26.9052	−1.52565	−0.762827	−	0.646603i	$-0.776189\pi$
$311$	−26.9052	−1.52565	−0.762827	+	0.646603i	$0.776189\pi$
$312$	2.05270	0.116211
$313$	23.2108	1.31195	0.655977	−	0.754781i	$-0.272257\pi$
$313$	23.2108	1.31195	0.655977	+	0.754781i	$0.272257\pi$
$314$	−0.502553	−0.0283607
$315$	−0.572465	−0.0322547
$316$	0.771377	0.0433934
$317$	19.8022	1.11220	0.556100	−	0.831115i	$-0.312297\pi$
$317$	19.8022	1.11220	0.556100	+	0.831115i	$0.312297\pi$
$318$	−2.49863	−0.140116
$319$	15.5891	0.872822
$320$	2.34533	0.131108
$321$	−11.4090	−0.636788
$322$	1.52972	0.0852481
$323$	3.20608	0.178391
$324$	1.00000	0.0555556
$325$	−1.02748	−0.0569943
$326$	−6.32513	−0.350317
$327$	−17.5802	−0.972188
$328$	3.76878	0.208096
$329$	0.726640	0.0400610
$330$	10.2981	0.566889
$331$	−0.207563	−0.0114087	−0.00570434	−	0.999984i	$-0.501816\pi$
$331$	−0.207563	−0.0114087	−0.00570434	+	0.999984i	$0.501816\pi$
$332$	−16.0036	−0.878311
$333$	2.99469	0.164108
$334$	−9.75443	−0.533739
$335$	20.8284	1.13797
$336$	−0.244087	−0.0133161
$337$	2.36065	0.128593	0.0642963	−	0.997931i	$-0.479520\pi$
$337$	2.36065	0.128593	0.0642963	+	0.997931i	$0.479520\pi$
$338$	8.78644	0.477919
$339$	6.87393	0.373341
$340$	−2.34533	−0.127193
$341$	18.7367	1.01465
$342$	3.20608	0.173365
$343$	3.40268	0.183728
$344$	−5.24504	−0.282794
$345$	14.6984	0.791336
$346$	22.7714	1.22420
$347$	−3.40020	−0.182532	−0.0912660	−	0.995827i	$-0.529091\pi$
$347$	−3.40020	−0.182532	−0.0912660	+	0.995827i	$0.529091\pi$
$348$	−3.55033	−0.190318
$349$	28.1213	1.50530	0.752651	−	0.658420i	$-0.228775\pi$
$349$	28.1213	1.50530	0.752651	+	0.658420i	$0.228775\pi$
$350$	0.122178	0.00653070
$351$	−2.05270	−0.109565
$352$	4.39089	0.234035
$353$	19.4076	1.03296	0.516482	−	0.856298i	$-0.327241\pi$
$353$	19.4076	1.03296	0.516482	+	0.856298i	$0.327241\pi$
$354$	−1.00000	−0.0531494
$355$	15.0134	0.796826
$356$	−5.53517	−0.293363
$357$	0.244087	0.0129185
$358$	15.4874	0.818536
$359$	−13.3119	−0.702575	−0.351288	−	0.936268i	$-0.614256\pi$
$359$	−13.3119	−0.702575	−0.351288	+	0.936268i	$0.614256\pi$
$360$	−2.34533	−0.123609
$361$	−8.72107	−0.459004
$362$	−25.3733	−1.33359
$363$	8.27989	0.434581
$364$	0.501037	0.0262615
$365$	−5.12069	−0.268029
$366$	−7.35455	−0.384428
$367$	−11.2895	−0.589308	−0.294654	−	0.955604i	$-0.595204\pi$
$367$	−11.2895	−0.589308	−0.294654	+	0.955604i	$0.595204\pi$
$368$	6.26711	0.326696
$369$	−3.76878	−0.196195
$370$	−7.02352	−0.365135
$371$	−0.609885	−0.0316636
$372$	−4.26717	−0.221243
$373$	4.08603	0.211567	0.105783	−	0.994389i	$-0.466265\pi$
$373$	4.08603	0.211567	0.105783	+	0.994389i	$0.466265\pi$
$374$	−4.39089	−0.227047
$375$	−10.5527	−0.544938
$376$	2.97697	0.153525
$377$	7.28775	0.375338
$378$	0.244087	0.0125545
$379$	−29.4311	−1.51177	−0.755886	−	0.654703i	$-0.772794\pi$
$379$	−29.4311	−1.51177	−0.755886	+	0.654703i	$0.772794\pi$
$380$	−7.51929	−0.385732
$381$	−2.11142	−0.108171
$382$	19.4985	0.997628
$383$	−20.4119	−1.04300	−0.521501	−	0.853251i	$-0.674628\pi$
$383$	−20.4119	−1.04300	−0.521501	+	0.853251i	$0.674628\pi$
$384$	−1.00000	−0.0510310
$385$	2.51363	0.128106
$386$	−2.34396	−0.119304
$387$	5.24504	0.266620
$388$	−5.16986	−0.262460
$389$	5.80273	0.294210	0.147105	−	0.989121i	$-0.453004\pi$
$389$	5.80273	0.294210	0.147105	+	0.989121i	$0.453004\pi$
$390$	4.81424	0.243779
$391$	−6.26711	−0.316941
$392$	6.94042	0.350544
$393$	−18.3512	−0.925694
$394$	−22.6806	−1.14263
$395$	1.80913	0.0910272
$396$	−4.39089	−0.220650
$397$	9.66372	0.485008	0.242504	−	0.970150i	$-0.422031\pi$
$397$	9.66372	0.485008	0.242504	+	0.970150i	$0.422031\pi$
$398$	−9.89201	−0.495842
$399$	0.782563	0.0391772
$400$	0.500551	0.0250275
$401$	−1.60858	−0.0803289	−0.0401644	−	0.999193i	$-0.512788\pi$
$401$	−1.60858	−0.0803289	−0.0401644	+	0.999193i	$0.512788\pi$
$402$	−8.88079	−0.442934
$403$	8.75921	0.436327
$404$	−7.23403	−0.359907
$405$	2.34533	0.116540
$406$	−0.866591	−0.0430082
$407$	−13.1493	−0.651788
$408$	1.00000	0.0495074
$409$	17.1670	0.848856	0.424428	−	0.905462i	$-0.360475\pi$
$409$	17.1670	0.848856	0.424428	+	0.905462i	$0.360475\pi$
$410$	8.83900	0.436527
$411$	−15.2719	−0.753308
$412$	−9.82845	−0.484213
$413$	−0.244087	−0.0120108
$414$	−6.26711	−0.308012
$415$	−37.5336	−1.84245
$416$	2.05270	0.100642
$417$	−20.2337	−0.990849
$418$	−14.0775	−0.688554
$419$	15.2397	0.744506	0.372253	−	0.928131i	$-0.378585\pi$
$419$	15.2397	0.744506	0.372253	+	0.928131i	$0.378585\pi$
$420$	−0.572465	−0.0279334
$421$	16.0509	0.782275	0.391138	−	0.920332i	$-0.372082\pi$
$421$	16.0509	0.782275	0.391138	+	0.920332i	$0.372082\pi$
$422$	18.3306	0.892322
$423$	−2.97697	−0.144745
$424$	−2.49863	−0.121344
$425$	−0.500551	−0.0242803
$426$	−6.40140	−0.310149
$427$	−1.79515	−0.0868735
$428$	−11.4090	−0.551474
$429$	9.01316	0.435159
$430$	−12.3013	−0.593222
$431$	3.87617	0.186708	0.0933542	−	0.995633i	$-0.470241\pi$
$431$	3.87617	0.186708	0.0933542	+	0.995633i	$0.470241\pi$
$432$	1.00000	0.0481125
$433$	3.85921	0.185462	0.0927309	−	0.995691i	$-0.470440\pi$
$433$	3.85921	0.185462	0.0927309	+	0.995691i	$0.470440\pi$
$434$	−1.04156	−0.0499966
$435$	−8.32668	−0.399234
$436$	−17.5802	−0.841939
$437$	−20.0928	−0.961171
$438$	2.18336	0.104325
$439$	7.92265	0.378127	0.189064	−	0.981965i	$-0.439455\pi$
$439$	7.92265	0.378127	0.189064	+	0.981965i	$0.439455\pi$
$440$	10.2981	0.490941
$441$	−6.94042	−0.330496
$442$	−2.05270	−0.0976368
$443$	−17.9781	−0.854163	−0.427082	−	0.904213i	$-0.640458\pi$
$443$	−17.9781	−0.854163	−0.427082	+	0.904213i	$0.640458\pi$
$444$	2.99469	0.142122
$445$	−12.9818	−0.615395
$446$	−2.97345	−0.140797
$447$	9.86871	0.466774
$448$	−0.244087	−0.0115320
$449$	4.38989	0.207172	0.103586	−	0.994621i	$-0.466968\pi$
$449$	4.38989	0.207172	0.103586	+	0.994621i	$0.466968\pi$
$450$	−0.500551	−0.0235962
$451$	16.5483	0.779227
$452$	6.87393	0.323323
$453$	−8.32774	−0.391271
$454$	12.2822	0.576431
$455$	1.17510	0.0550893
$456$	3.20608	0.150138
$457$	−34.4349	−1.61079	−0.805397	−	0.592735i	$-0.798048\pi$
$457$	−34.4349	−1.61079	−0.805397	+	0.592735i	$0.798048\pi$
$458$	−3.89318	−0.181916
$459$	−1.00000	−0.0466760
$460$	14.6984	0.685317
$461$	28.6982	1.33661	0.668303	−	0.743889i	$-0.267021\pi$
$461$	28.6982	1.33661	0.668303	+	0.743889i	$0.267021\pi$
$462$	−1.07176	−0.0498628
$463$	9.78563	0.454777	0.227388	−	0.973804i	$-0.426981\pi$
$463$	9.78563	0.454777	0.227388	+	0.973804i	$0.426981\pi$
$464$	−3.55033	−0.164820
$465$	−10.0079	−0.464105
$466$	15.5629	0.720939
$467$	−34.6088	−1.60150	−0.800751	−	0.598997i	$-0.795566\pi$
$467$	−34.6088	−1.60150	−0.800751	+	0.598997i	$0.795566\pi$
$468$	−2.05270	−0.0948859
$469$	−2.16769	−0.100095
$470$	6.98196	0.322054
$471$	0.502553	0.0231564
$472$	−1.00000	−0.0460287
$473$	−23.0304	−1.05894
$474$	−0.771377	−0.0354305
$475$	−1.60480	−0.0736335
$476$	0.244087	0.0111877
$477$	2.49863	0.114404
$478$	−19.3551	−0.885284
$479$	35.3267	1.61412	0.807059	−	0.590471i	$-0.201058\pi$
$479$	35.3267	1.61412	0.807059	+	0.590471i	$0.201058\pi$
$480$	−2.34533	−0.107049
$481$	−6.14718	−0.280287
$482$	−23.0940	−1.05190
$483$	−1.52972	−0.0696048
$484$	8.27989	0.376358
$485$	−12.1250	−0.550568
$486$	−1.00000	−0.0453609
$487$	0.413367	0.0187314	0.00936572	−	0.999956i	$-0.497019\pi$
$487$	0.413367	0.0187314	0.00936572	+	0.999956i	$0.497019\pi$
$488$	−7.35455	−0.332925
$489$	6.32513	0.286032
$490$	16.2775	0.735345
$491$	−18.5001	−0.834897	−0.417449	−	0.908701i	$-0.637076\pi$
$491$	−18.5001	−0.834897	−0.417449	+	0.908701i	$0.637076\pi$
$492$	−3.76878	−0.169909
$493$	3.55033	0.159899
$494$	−6.58110	−0.296098
$495$	−10.2981	−0.462863
$496$	−4.26717	−0.191602
$497$	−1.56250	−0.0700877
$498$	16.0036	0.717138
$499$	−2.83079	−0.126724	−0.0633618	−	0.997991i	$-0.520182\pi$
$499$	−2.83079	−0.126724	−0.0633618	+	0.997991i	$0.520182\pi$
$500$	−10.5527	−0.471930
$501$	9.75443	0.435796
$502$	12.0132	0.536177
$503$	−21.4909	−0.958232	−0.479116	−	0.877751i	$-0.659043\pi$
$503$	−21.4909	−0.958232	−0.479116	+	0.877751i	$0.659043\pi$
$504$	0.244087	0.0108725
$505$	−16.9662	−0.754984
$506$	27.5182	1.22333
$507$	−8.78644	−0.390219
$508$	−2.11142	−0.0936790
$509$	27.0573	1.19930	0.599648	−	0.800264i	$-0.295307\pi$
$509$	27.0573	1.19930	0.599648	+	0.800264i	$0.295307\pi$
$510$	2.34533	0.103853
$511$	0.532931	0.0235755
$512$	−1.00000	−0.0441942
$513$	−3.20608	−0.141552
$514$	−23.5780	−1.03998
$515$	−23.0509	−1.01574
$516$	5.24504	0.230900
$517$	13.0715	0.574885
$518$	0.730966	0.0321168
$519$	−22.7714	−0.999552
$520$	4.81424	0.211118
$521$	−6.13990	−0.268994	−0.134497	−	0.990914i	$-0.542942\pi$
$521$	−6.13990	−0.268994	−0.134497	+	0.990914i	$0.542942\pi$
$522$	3.55033	0.155394
$523$	2.07676	0.0908105	0.0454053	−	0.998969i	$-0.485542\pi$
$523$	2.07676	0.0908105	0.0454053	+	0.998969i	$0.485542\pi$
$524$	−18.3512	−0.801675
$525$	−0.122178	−0.00533229
$526$	0.246600	0.0107523
$527$	4.26717	0.185881
$528$	−4.39089	−0.191089
$529$	16.2767	0.707682
$530$	−5.86010	−0.254547
$531$	1.00000	0.0433963
$532$	0.782563	0.0339284
$533$	7.73615	0.335090
$534$	5.53517	0.239530
$535$	−26.7578	−1.15684
$536$	−8.88079	−0.383592
$537$	−15.4874	−0.668332
$538$	19.3872	0.835841
$539$	30.4746	1.31263
$540$	2.34533	0.100927
$541$	23.0739	0.992027	0.496013	−	0.868315i	$-0.334797\pi$
$541$	23.0739	0.992027	0.496013	+	0.868315i	$0.334797\pi$
$542$	27.2887	1.17215
$543$	25.3733	1.08887
$544$	1.00000	0.0428746
$545$	−41.2313	−1.76616
$546$	−0.501037	−0.0214424
$547$	−26.2713	−1.12328	−0.561639	−	0.827382i	$-0.689829\pi$
$547$	−26.2713	−1.12328	−0.561639	+	0.827382i	$0.689829\pi$
$548$	−15.2719	−0.652384
$549$	7.35455	0.313884
$550$	2.19786	0.0937171
$551$	11.3826	0.484916
$552$	−6.26711	−0.266746
$553$	−0.188284	−0.00800663
$554$	−7.58671	−0.322328
$555$	7.02352	0.298132
$556$	−20.2337	−0.858100
$557$	20.3061	0.860395	0.430198	−	0.902735i	$-0.358444\pi$
$557$	20.3061	0.860395	0.430198	+	0.902735i	$0.358444\pi$
$558$	4.26717	0.180644
$559$	−10.7665	−0.455373
$560$	−0.572465	−0.0241910
$561$	4.39089	0.185383
$562$	11.4719	0.483915
$563$	−22.6281	−0.953660	−0.476830	−	0.878996i	$-0.658214\pi$
$563$	−22.6281	−0.953660	−0.476830	+	0.878996i	$0.658214\pi$
$564$	−2.97697	−0.125353
$565$	16.1216	0.678241
$566$	−27.0012	−1.13495
$567$	−0.244087	−0.0102507
$568$	−6.40140	−0.268597
$569$	−35.7443	−1.49848	−0.749239	−	0.662300i	$-0.769580\pi$
$569$	−35.7443	−1.49848	−0.749239	+	0.662300i	$0.769580\pi$
$570$	7.51929	0.314948
$571$	32.4623	1.35851	0.679253	−	0.733904i	$-0.262304\pi$
$571$	32.4623	1.35851	0.679253	+	0.733904i	$0.262304\pi$
$572$	9.01316	0.376859
$573$	−19.4985	−0.814560
$574$	−0.919911	−0.0383963
$575$	3.13701	0.130822
$576$	1.00000	0.0416667
$577$	19.9918	0.832268	0.416134	−	0.909303i	$-0.363385\pi$
$577$	19.9918	0.832268	0.416134	+	0.909303i	$0.363385\pi$
$578$	−1.00000	−0.0415945
$579$	2.34396	0.0974115
$580$	−8.32668	−0.345747
$581$	3.90627	0.162060
$582$	5.16986	0.214298
$583$	−10.9712	−0.454381
$584$	2.18336	0.0903481
$585$	−4.81424	−0.199044
$586$	−4.10937	−0.169756
$587$	41.5926	1.71671	0.858355	−	0.513057i	$-0.171487\pi$
$587$	41.5926	1.71671	0.858355	+	0.513057i	$0.171487\pi$
$588$	−6.94042	−0.286218
$589$	13.6809	0.563711
$590$	−2.34533	−0.0965555
$591$	22.6806	0.932955
$592$	2.99469	0.123081
$593$	−25.9930	−1.06741	−0.533703	−	0.845672i	$-0.679200\pi$
$593$	−25.9930	−1.06741	−0.533703	+	0.845672i	$0.679200\pi$
$594$	4.39089	0.180160
$595$	0.572465	0.0234688
$596$	9.86871	0.404238
$597$	9.89201	0.404853
$598$	12.8645	0.526068
$599$	34.5918	1.41338	0.706692	−	0.707522i	$-0.250187\pi$
$599$	34.5918	1.41338	0.706692	+	0.707522i	$0.250187\pi$
$600$	−0.500551	−0.0204349
$601$	11.3750	0.463996	0.231998	−	0.972716i	$-0.425474\pi$
$601$	11.3750	0.463996	0.231998	+	0.972716i	$0.425474\pi$
$602$	1.28025	0.0521790
$603$	8.88079	0.361654
$604$	−8.32774	−0.338851
$605$	19.4190	0.789496
$606$	7.23403	0.293863
$607$	−18.9195	−0.767919	−0.383959	−	0.923350i	$-0.625440\pi$
$607$	−18.9195	−0.767919	−0.383959	+	0.923350i	$0.625440\pi$
$608$	3.20608	0.130024
$609$	0.866591	0.0351161
$610$	−17.2488	−0.698384
$611$	6.11081	0.247217
$612$	−1.00000	−0.0404226
$613$	−28.2821	−1.14230	−0.571151	−	0.820845i	$-0.693503\pi$
$613$	−28.2821	−1.14230	−0.571151	+	0.820845i	$0.693503\pi$
$614$	−24.2877	−0.980170
$615$	−8.83900	−0.356423
$616$	−1.07176	−0.0431825
$617$	36.2879	1.46089	0.730447	−	0.682969i	$-0.239312\pi$
$617$	36.2879	1.46089	0.730447	+	0.682969i	$0.239312\pi$
$618$	9.82845	0.395358
$619$	5.20904	0.209369	0.104684	−	0.994505i	$-0.466617\pi$
$619$	5.20904	0.209369	0.104684	+	0.994505i	$0.466617\pi$
$620$	−10.0079	−0.401927
$621$	6.26711	0.251491
$622$	26.9052	1.07880
$623$	1.35106	0.0541293
$624$	−2.05270	−0.0821736
$625$	−27.2522	−1.09009
$626$	−23.2108	−0.927692
$627$	14.0775	0.562202
$628$	0.502553	0.0200540
$629$	−2.99469	−0.119406
$630$	0.572465	0.0228075
$631$	15.0479	0.599046	0.299523	−	0.954089i	$-0.403173\pi$
$631$	15.0479	0.599046	0.299523	+	0.954089i	$0.403173\pi$
$632$	−0.771377	−0.0306837
$633$	−18.3306	−0.728578
$634$	−19.8022	−0.786445
$635$	−4.95196	−0.196513
$636$	2.49863	0.0990772
$637$	14.2466	0.564470
$638$	−15.5891	−0.617178
$639$	6.40140	0.253235
$640$	−2.34533	−0.0927071
$641$	−30.9576	−1.22275	−0.611376	−	0.791340i	$-0.709384\pi$
$641$	−30.9576	−1.22275	−0.611376	+	0.791340i	$0.709384\pi$
$642$	11.4090	0.450277
$643$	11.4319	0.450832	0.225416	−	0.974263i	$-0.427626\pi$
$643$	11.4319	0.450832	0.225416	+	0.974263i	$0.427626\pi$
$644$	−1.52972	−0.0602795
$645$	12.3013	0.484364
$646$	−3.20608	−0.126141
$647$	−8.07919	−0.317626	−0.158813	−	0.987309i	$-0.550767\pi$
$647$	−8.07919	−0.317626	−0.158813	+	0.987309i	$0.550767\pi$
$648$	−1.00000	−0.0392837
$649$	−4.39089	−0.172357
$650$	1.02748	0.0403010
$651$	1.04156	0.0408221
$652$	6.32513	0.247711
$653$	33.4871	1.31045	0.655226	−	0.755433i	$-0.272573\pi$
$653$	33.4871	1.31045	0.655226	+	0.755433i	$0.272573\pi$
$654$	17.5802	0.687441
$655$	−43.0395	−1.68169
$656$	−3.76878	−0.147146
$657$	−2.18336	−0.0851810
$658$	−0.726640	−0.0283274
$659$	−37.5601	−1.46313	−0.731566	−	0.681771i	$-0.761210\pi$
$659$	−37.5601	−1.46313	−0.731566	+	0.681771i	$0.761210\pi$
$660$	−10.2981	−0.400851
$661$	46.7839	1.81968	0.909842	−	0.414955i	$-0.136203\pi$
$661$	46.7839	1.81968	0.909842	+	0.414955i	$0.136203\pi$
$662$	0.207563	0.00806715
$663$	2.05270	0.0797201
$664$	16.0036	0.621059
$665$	1.83536	0.0711724
$666$	−2.99469	−0.116042
$667$	−22.2503	−0.861536
$668$	9.75443	0.377410
$669$	2.97345	0.114960
$670$	−20.8284	−0.804669
$671$	−32.2930	−1.24666
$672$	0.244087	0.00941588
$673$	46.1030	1.77714	0.888569	−	0.458742i	$-0.151700\pi$
$673$	46.1030	1.77714	0.888569	+	0.458742i	$0.151700\pi$
$674$	−2.36065	−0.0909287
$675$	0.500551	0.0192662
$676$	−8.78644	−0.337940
$677$	−42.9019	−1.64885	−0.824427	−	0.565968i	$-0.808503\pi$
$677$	−42.9019	−1.64885	−0.824427	+	0.565968i	$0.808503\pi$
$678$	−6.87393	−0.263992
$679$	1.26190	0.0484272
$680$	2.34533	0.0899391
$681$	−12.2822	−0.470654
$682$	−18.7367	−0.717464
$683$	−21.6194	−0.827242	−0.413621	−	0.910449i	$-0.635736\pi$
$683$	−21.6194	−0.827242	−0.413621	+	0.910449i	$0.635736\pi$
$684$	−3.20608	−0.122587
$685$	−35.8176	−1.36852
$686$	−3.40268	−0.129915
$687$	3.89318	0.148534
$688$	5.24504	0.199965
$689$	−5.12893	−0.195397
$690$	−14.6984	−0.559559
$691$	−9.53155	−0.362597	−0.181299	−	0.983428i	$-0.558030\pi$
$691$	−9.53155	−0.362597	−0.181299	+	0.983428i	$0.558030\pi$
$692$	−22.7714	−0.865637
$693$	1.07176	0.0407128
$694$	3.40020	0.129070
$695$	−47.4546	−1.80006
$696$	3.55033	0.134575
$697$	3.76878	0.142753
$698$	−28.1213	−1.06441
$699$	−15.5629	−0.588644
$700$	−0.122178	−0.00461790
$701$	−7.24580	−0.273670	−0.136835	−	0.990594i	$-0.543693\pi$
$701$	−7.24580	−0.273670	−0.136835	+	0.990594i	$0.543693\pi$
$702$	2.05270	0.0774740
$703$	−9.60120	−0.362116
$704$	−4.39089	−0.165488
$705$	−6.98196	−0.262956
$706$	−19.4076	−0.730415
$707$	1.76574	0.0664074
$708$	1.00000	0.0375823
$709$	16.2889	0.611741	0.305871	−	0.952073i	$-0.401052\pi$
$709$	16.2889	0.611741	0.305871	+	0.952073i	$0.401052\pi$
$710$	−15.0134	−0.563441
$711$	0.771377	0.0289289
$712$	5.53517	0.207439
$713$	−26.7428	−1.00153
$714$	−0.244087	−0.00913474
$715$	21.1388	0.790546
$716$	−15.4874	−0.578792
$717$	19.3551	0.722831
$718$	13.3119	0.496796
$719$	−3.74847	−0.139794	−0.0698972	−	0.997554i	$-0.522267\pi$
$719$	−3.74847	−0.139794	−0.0698972	+	0.997554i	$0.522267\pi$
$720$	2.34533	0.0874051
$721$	2.39900	0.0893434
$722$	8.72107	0.324565
$723$	23.0940	0.858876
$724$	25.3733	0.942991
$725$	−1.77712	−0.0660006
$726$	−8.27989	−0.307295
$727$	31.5778	1.17116	0.585579	−	0.810616i	$-0.300867\pi$
$727$	31.5778	1.17116	0.585579	+	0.810616i	$0.300867\pi$
$728$	−0.501037	−0.0185697
$729$	1.00000	0.0370370
$730$	5.12069	0.189525
$731$	−5.24504	−0.193995
$732$	7.35455	0.271832
$733$	28.5277	1.05369	0.526847	−	0.849960i	$-0.323374\pi$
$733$	28.5277	1.05369	0.526847	+	0.849960i	$0.323374\pi$
$734$	11.2895	0.416704
$735$	−16.2775	−0.600406
$736$	−6.26711	−0.231009
$737$	−38.9946	−1.43638
$738$	3.76878	0.138731
$739$	−5.91129	−0.217450	−0.108725	−	0.994072i	$-0.534677\pi$
$739$	−5.91129	−0.217450	−0.108725	+	0.994072i	$0.534677\pi$
$740$	7.02352	0.258190
$741$	6.58110	0.241763
$742$	0.609885	0.0223896
$743$	−40.8738	−1.49951	−0.749756	−	0.661714i	$-0.769829\pi$
$743$	−40.8738	−1.49951	−0.749756	+	0.661714i	$0.769829\pi$
$744$	4.26717	0.156442
$745$	23.1453	0.847979
$746$	−4.08603	−0.149600
$747$	−16.0036	−0.585540
$748$	4.39089	0.160547
$749$	2.78479	0.101754
$750$	10.5527	0.385329
$751$	−32.9763	−1.20332	−0.601662	−	0.798751i	$-0.705495\pi$
$751$	−32.9763	−1.20332	−0.601662	+	0.798751i	$0.705495\pi$
$752$	−2.97697	−0.108559
$753$	−12.0132	−0.437786
$754$	−7.28775	−0.265404
$755$	−19.5313	−0.710815
$756$	−0.244087	−0.00887738
$757$	−13.3910	−0.486706	−0.243353	−	0.969938i	$-0.578247\pi$
$757$	−13.3910	−0.486706	−0.243353	+	0.969938i	$0.578247\pi$
$758$	29.4311	1.06898
$759$	−27.5182	−0.998846
$760$	7.51929	0.272753
$761$	−22.0729	−0.800144	−0.400072	−	0.916484i	$-0.631015\pi$
$761$	−22.0729	−0.800144	−0.400072	+	0.916484i	$0.631015\pi$
$762$	2.11142	0.0764886
$763$	4.29111	0.155349
$764$	−19.4985	−0.705429
$765$	−2.34533	−0.0847954
$766$	20.4119	0.737514
$767$	−2.05270	−0.0741186
$768$	1.00000	0.0360844
$769$	30.0689	1.08431	0.542157	−	0.840277i	$-0.317608\pi$
$769$	30.0689	1.08431	0.542157	+	0.840277i	$0.317608\pi$
$770$	−2.51363	−0.0905848
$771$	23.5780	0.849140
$772$	2.34396	0.0843609
$773$	−42.6620	−1.53444	−0.767222	−	0.641381i	$-0.778362\pi$
$773$	−42.6620	−1.53444	−0.767222	+	0.641381i	$0.778362\pi$
$774$	−5.24504	−0.188529
$775$	−2.13594	−0.0767251
$776$	5.16986	0.185587
$777$	−0.730966	−0.0262233
$778$	−5.80273	−0.208038
$779$	12.0830	0.432918
$780$	−4.81424	−0.172377
$781$	−28.1078	−1.00578
$782$	6.26711	0.224111
$783$	−3.55033	−0.126878
$784$	−6.94042	−0.247872
$785$	1.17865	0.0420678
$786$	18.3512	0.654565
$787$	−20.2291	−0.721089	−0.360545	−	0.932742i	$-0.617409\pi$
$787$	−20.2291	−0.721089	−0.360545	+	0.932742i	$0.617409\pi$
$788$	22.6806	0.807963
$789$	−0.246600	−0.00877921
$790$	−1.80913	−0.0643660
$791$	−1.67784	−0.0596571
$792$	4.39089	0.156023
$793$	−15.0967	−0.536098
$794$	−9.66372	−0.342953
$795$	5.86010	0.207836
$796$	9.89201	0.350613
$797$	−6.30987	−0.223507	−0.111754	−	0.993736i	$-0.535647\pi$
$797$	−6.30987	−0.223507	−0.111754	+	0.993736i	$0.535647\pi$
$798$	−0.782563	−0.0277024
$799$	2.97697	0.105318
$800$	−0.500551	−0.0176971
$801$	−5.53517	−0.195575
$802$	1.60858	0.0568011
$803$	9.58689	0.338314
$804$	8.88079	0.313201
$805$	−3.58770	−0.126450
$806$	−8.75921	−0.308530
$807$	−19.3872	−0.682461
$808$	7.23403	0.254492
$809$	10.8841	0.382666	0.191333	−	0.981525i	$-0.438719\pi$
$809$	10.8841	0.382666	0.191333	+	0.981525i	$0.438719\pi$
$810$	−2.34533	−0.0824063
$811$	38.9411	1.36741	0.683704	−	0.729760i	$-0.260368\pi$
$811$	38.9411	1.36741	0.683704	+	0.729760i	$0.260368\pi$
$812$	0.866591	0.0304114
$813$	−27.2887	−0.957058
$814$	13.1493	0.460884
$815$	14.8345	0.519629
$816$	−1.00000	−0.0350070
$817$	−16.8160	−0.588317
$818$	−17.1670	−0.600232
$819$	0.501037	0.0175077
$820$	−8.83900	−0.308671
$821$	−45.3109	−1.58136	−0.790680	−	0.612230i	$-0.790273\pi$
$821$	−45.3109	−1.58136	−0.790680	+	0.612230i	$0.790273\pi$
$822$	15.2719	0.532669
$823$	32.5363	1.13414	0.567072	−	0.823668i	$-0.308076\pi$
$823$	32.5363	1.13414	0.567072	+	0.823668i	$0.308076\pi$
$824$	9.82845	0.342390
$825$	−2.19786	−0.0765197
$826$	0.244087	0.00849289
$827$	26.0894	0.907218	0.453609	−	0.891201i	$-0.350136\pi$
$827$	26.0894	0.907218	0.453609	+	0.891201i	$0.350136\pi$
$828$	6.26711	0.217797
$829$	45.8199	1.59139	0.795696	−	0.605696i	$-0.207105\pi$
$829$	45.8199	1.59139	0.795696	+	0.605696i	$0.207105\pi$
$830$	37.5336	1.30281
$831$	7.58671	0.263180
$832$	−2.05270	−0.0711644
$833$	6.94042	0.240471
$834$	20.2337	0.700636
$835$	22.8773	0.791702
$836$	14.0775	0.486881
$837$	−4.26717	−0.147495
$838$	−15.2397	−0.526445
$839$	10.6076	0.366213	0.183107	−	0.983093i	$-0.441385\pi$
$839$	10.6076	0.366213	0.183107	+	0.983093i	$0.441385\pi$
$840$	0.572465	0.0197519
$841$	−16.3951	−0.565350
$842$	−16.0509	−0.553152
$843$	−11.4719	−0.395115
$844$	−18.3306	−0.630967
$845$	−20.6071	−0.708904
$846$	2.97697	0.102350
$847$	−2.02102	−0.0694429
$848$	2.49863	0.0858033
$849$	27.0012	0.926680
$850$	0.500551	0.0171687
$851$	18.7680	0.643360
$852$	6.40140	0.219308
$853$	19.2095	0.657720	0.328860	−	0.944379i	$-0.393336\pi$
$853$	19.2095	0.657720	0.328860	+	0.944379i	$0.393336\pi$
$854$	1.79515	0.0614289
$855$	−7.51929	−0.257154
$856$	11.4090	0.389951
$857$	−24.8137	−0.847619	−0.423809	−	0.905751i	$-0.639307\pi$
$857$	−24.8137	−0.847619	−0.423809	+	0.905751i	$0.639307\pi$
$858$	−9.01316	−0.307704
$859$	−7.50683	−0.256130	−0.128065	−	0.991766i	$-0.540877\pi$
$859$	−7.50683	−0.256130	−0.128065	+	0.991766i	$0.540877\pi$
$860$	12.3013	0.419472
$861$	0.919911	0.0313505
$862$	−3.87617	−0.132023
$863$	−1.50782	−0.0513267	−0.0256633	−	0.999671i	$-0.508170\pi$
$863$	−1.50782	−0.0513267	−0.0256633	+	0.999671i	$0.508170\pi$
$864$	−1.00000	−0.0340207
$865$	−53.4063	−1.81587
$866$	−3.85921	−0.131141
$867$	1.00000	0.0339618
$868$	1.04156	0.0353530
$869$	−3.38703	−0.114897
$870$	8.32668	0.282301
$871$	−18.2296	−0.617686
$872$	17.5802	0.595341
$873$	−5.16986	−0.174973
$874$	20.0928	0.679650
$875$	2.57577	0.0870771
$876$	−2.18336	−0.0737689
$877$	−11.4577	−0.386899	−0.193450	−	0.981110i	$-0.561968\pi$
$877$	−11.4577	−0.386899	−0.193450	+	0.981110i	$0.561968\pi$
$878$	−7.92265	−0.267376
$879$	4.10937	0.138606
$880$	−10.2981	−0.347147
$881$	9.90255	0.333625	0.166813	−	0.985989i	$-0.446652\pi$
$881$	9.90255	0.333625	0.166813	+	0.985989i	$0.446652\pi$
$882$	6.94042	0.233696
$883$	−14.5910	−0.491027	−0.245514	−	0.969393i	$-0.578957\pi$
$883$	−14.5910	−0.491027	−0.245514	+	0.969393i	$0.578957\pi$
$884$	2.05270	0.0690396
$885$	2.34533	0.0788372
$886$	17.9781	0.603985
$887$	40.2169	1.35035	0.675176	−	0.737657i	$-0.264068\pi$
$887$	40.2169	1.35035	0.675176	+	0.737657i	$0.264068\pi$
$888$	−2.99469	−0.100495
$889$	0.515371	0.0172850
$890$	12.9818	0.435150
$891$	−4.39089	−0.147100
$892$	2.97345	0.0995585
$893$	9.54438	0.319391
$894$	−9.86871	−0.330059
$895$	−36.3231	−1.21415
$896$	0.244087	0.00815439
$897$	−12.8645	−0.429532
$898$	−4.38989	−0.146492
$899$	15.1499	0.505277
$900$	0.500551	0.0166850
$901$	−2.49863	−0.0832415
$902$	−16.5483	−0.550997
$903$	−1.28025	−0.0426040
$904$	−6.87393	−0.228624
$905$	59.5086	1.97813
$906$	8.32774	0.276671
$907$	−7.53193	−0.250094	−0.125047	−	0.992151i	$-0.539908\pi$
$907$	−7.53193	−0.250094	−0.125047	+	0.992151i	$0.539908\pi$
$908$	−12.2822	−0.407599
$909$	−7.23403	−0.239938
$910$	−1.17510	−0.0389540
$911$	−13.4786	−0.446567	−0.223283	−	0.974754i	$-0.571678\pi$
$911$	−13.4786	−0.446567	−0.223283	+	0.974754i	$0.571678\pi$
$912$	−3.20608	−0.106164
$913$	70.2699	2.32559
$914$	34.4349	1.13900
$915$	17.2488	0.570228
$916$	3.89318	0.128634
$917$	4.47929	0.147919
$918$	1.00000	0.0330049
$919$	−11.5838	−0.382114	−0.191057	−	0.981579i	$-0.561191\pi$
$919$	−11.5838	−0.382114	−0.191057	+	0.981579i	$0.561191\pi$
$920$	−14.6984	−0.484592
$921$	24.2877	0.800306
$922$	−28.6982	−0.945123
$923$	−13.1401	−0.432512
$924$	1.07176	0.0352583
$925$	1.49899	0.0492866
$926$	−9.78563	−0.321576
$927$	−9.82845	−0.322808
$928$	3.55033	0.116545
$929$	−19.6975	−0.646253	−0.323127	−	0.946356i	$-0.604734\pi$
$929$	−19.6975	−0.646253	−0.323127	+	0.946356i	$0.604734\pi$
$930$	10.0079	0.328172
$931$	22.2515	0.729264
$932$	−15.5629	−0.509781
$933$	−26.9052	−0.880837
$934$	34.6088	1.13243
$935$	10.2981	0.336782
$936$	2.05270	0.0670945
$937$	−45.7558	−1.49478	−0.747389	−	0.664387i	$-0.768693\pi$
$937$	−45.7558	−1.49478	−0.747389	+	0.664387i	$0.768693\pi$
$938$	2.16769	0.0707776
$939$	23.2108	0.757457
$940$	−6.98196	−0.227726
$941$	15.4069	0.502251	0.251126	−	0.967955i	$-0.419199\pi$
$941$	15.4069	0.502251	0.251126	+	0.967955i	$0.419199\pi$
$942$	−0.502553	−0.0163740
$943$	−23.6193	−0.769151
$944$	1.00000	0.0325472
$945$	−0.572465	−0.0186223
$946$	23.0304	0.748782
$947$	4.92088	0.159907	0.0799535	−	0.996799i	$-0.474523\pi$
$947$	4.92088	0.159907	0.0799535	+	0.996799i	$0.474523\pi$
$948$	0.771377	0.0250532
$949$	4.48178	0.145485
$950$	1.60480	0.0520667
$951$	19.8022	0.642129
$952$	−0.244087	−0.00791092
$953$	19.0827	0.618149	0.309075	−	0.951038i	$-0.399981\pi$
$953$	19.0827	0.618149	0.309075	+	0.951038i	$0.399981\pi$
$954$	−2.49863	−0.0808962
$955$	−45.7302	−1.47980
$956$	19.3551	0.625990
$957$	15.5891	0.503924
$958$	−35.3267	−1.14135
$959$	3.72768	0.120373
$960$	2.34533	0.0756950
$961$	−12.7912	−0.412621
$962$	6.14718	0.198193
$963$	−11.4090	−0.367650
$964$	23.0940	0.743809
$965$	5.49734	0.176966
$966$	1.52972	0.0492180
$967$	30.4883	0.980437	0.490218	−	0.871600i	$-0.336917\pi$
$967$	30.4883	0.980437	0.490218	+	0.871600i	$0.336917\pi$
$968$	−8.27989	−0.266126
$969$	3.20608	0.102994
$970$	12.1250	0.389310
$971$	19.0627	0.611751	0.305876	−	0.952072i	$-0.401051\pi$
$971$	19.0627	0.611751	0.305876	+	0.952072i	$0.401051\pi$
$972$	1.00000	0.0320750
$973$	4.93879	0.158330
$974$	−0.413367	−0.0132451
$975$	−1.02748	−0.0329057
$976$	7.35455	0.235413
$977$	−2.74631	−0.0878622	−0.0439311	−	0.999035i	$-0.513988\pi$
$977$	−2.74631	−0.0878622	−0.0439311	+	0.999035i	$0.513988\pi$
$978$	−6.32513	−0.202255
$979$	24.3043	0.776768
$980$	−16.2775	−0.519967
$981$	−17.5802	−0.561293
$982$	18.5001	0.590361
$983$	−15.5613	−0.496328	−0.248164	−	0.968718i	$-0.579827\pi$
$983$	−15.5613	−0.496328	−0.248164	+	0.968718i	$0.579827\pi$
$984$	3.76878	0.120144
$985$	53.1934	1.69488
$986$	−3.55033	−0.113066
$987$	0.726640	0.0231292
$988$	6.58110	0.209373
$989$	32.8712	1.04524
$990$	10.2981	0.327294
$991$	−2.67530	−0.0849838	−0.0424919	−	0.999097i	$-0.513530\pi$
$991$	−2.67530	−0.0849838	−0.0424919	+	0.999097i	$0.513530\pi$
$992$	4.26717	0.135483
$993$	−0.207563	−0.00658680
$994$	1.56250	0.0495595
$995$	23.2000	0.735489
$996$	−16.0036	−0.507093
$997$	11.6565	0.369166	0.184583	−	0.982817i	$-0.440907\pi$
$997$	11.6565	0.369166	0.184583	+	0.982817i	$0.440907\pi$
$998$	2.83079	0.0896071
$999$	2.99469	0.0947477

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.y.1.8	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.y.1.8	✓	10	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.34533 q^{5} -1.00000 q^{6} -0.244087 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.34533 q^{5} -1.00000 q^{6} -0.244087 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.34533 q^{10} -4.39089 q^{11} +1.00000 q^{12} -2.05270 q^{13} +0.244087 q^{14} +2.34533 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} -3.20608 q^{19} +2.34533 q^{20} -0.244087 q^{21} +4.39089 q^{22} +6.26711 q^{23} -1.00000 q^{24} +0.500551 q^{25} +2.05270 q^{26} +1.00000 q^{27} -0.244087 q^{28} -3.55033 q^{29} -2.34533 q^{30} -4.26717 q^{31} -1.00000 q^{32} -4.39089 q^{33} +1.00000 q^{34} -0.572465 q^{35} +1.00000 q^{36} +2.99469 q^{37} +3.20608 q^{38} -2.05270 q^{39} -2.34533 q^{40} -3.76878 q^{41} +0.244087 q^{42} +5.24504 q^{43} -4.39089 q^{44} +2.34533 q^{45} -6.26711 q^{46} -2.97697 q^{47} +1.00000 q^{48} -6.94042 q^{49} -0.500551 q^{50} -1.00000 q^{51} -2.05270 q^{52} +2.49863 q^{53} -1.00000 q^{54} -10.2981 q^{55} +0.244087 q^{56} -3.20608 q^{57} +3.55033 q^{58} +1.00000 q^{59} +2.34533 q^{60} +7.35455 q^{61} +4.26717 q^{62} -0.244087 q^{63} +1.00000 q^{64} -4.81424 q^{65} +4.39089 q^{66} +8.88079 q^{67} -1.00000 q^{68} +6.26711 q^{69} +0.572465 q^{70} +6.40140 q^{71} -1.00000 q^{72} -2.18336 q^{73} -2.99469 q^{74} +0.500551 q^{75} -3.20608 q^{76} +1.07176 q^{77} +2.05270 q^{78} +0.771377 q^{79} +2.34533 q^{80} +1.00000 q^{81} +3.76878 q^{82} -16.0036 q^{83} -0.244087 q^{84} -2.34533 q^{85} -5.24504 q^{86} -3.55033 q^{87} +4.39089 q^{88} -5.53517 q^{89} -2.34533 q^{90} +0.501037 q^{91} +6.26711 q^{92} -4.26717 q^{93} +2.97697 q^{94} -7.51929 q^{95} -1.00000 q^{96} -5.16986 q^{97} +6.94042 q^{98} -4.39089 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} + 10 q^{3} + 10 q^{4} - 2 q^{5} - 10 q^{6} - 6 q^{7} - 10 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 + 10 * q^3 + 10 * q^4 - 2 * q^5 - 10 * q^6 - 6 * q^7 - 10 * q^8 + 10 * q^9	\( 10 q - 10 q^{2} + 10 q^{3} + 10 q^{4} - 2 q^{5} - 10 q^{6} - 6 q^{7} - 10 q^{8} + 10 q^{9} + 2 q^{10} - 3 q^{11} + 10 q^{12} - 10 q^{13} + 6 q^{14} - 2 q^{15} + 10 q^{16} - 10 q^{17} - 10 q^{18} + 8 q^{19} - 2 q^{20} - 6 q^{21} + 3 q^{22} - 9 q^{23} - 10 q^{24} + 20 q^{25} + 10 q^{26} + 10 q^{27} - 6 q^{28} - 24 q^{29} + 2 q^{30} - 7 q^{31} - 10 q^{32} - 3 q^{33} + 10 q^{34} - 22 q^{35} + 10 q^{36} - 4 q^{37} - 8 q^{38} - 10 q^{39} + 2 q^{40} - 9 q^{41} + 6 q^{42} - 11 q^{43} - 3 q^{44} - 2 q^{45} + 9 q^{46} - 18 q^{47} + 10 q^{48} + 6 q^{49} - 20 q^{50} - 10 q^{51} - 10 q^{52} - 9 q^{53} - 10 q^{54} + q^{55} + 6 q^{56} + 8 q^{57} + 24 q^{58} + 10 q^{59} - 2 q^{60} - 25 q^{61} + 7 q^{62} - 6 q^{63} + 10 q^{64} - 28 q^{65} + 3 q^{66} + 2 q^{67} - 10 q^{68} - 9 q^{69} + 22 q^{70} - 30 q^{71} - 10 q^{72} - 11 q^{73} + 4 q^{74} + 20 q^{75} + 8 q^{76} + 4 q^{77} + 10 q^{78} + 3 q^{79} - 2 q^{80} + 10 q^{81} + 9 q^{82} - q^{83} - 6 q^{84} + 2 q^{85} + 11 q^{86} - 24 q^{87} + 3 q^{88} - 14 q^{89} + 2 q^{90} - 13 q^{91} - 9 q^{92} - 7 q^{93} + 18 q^{94} - 35 q^{95} - 10 q^{96} - 10 q^{97} - 6 q^{98} - 3 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 + 10 * q^3 + 10 * q^4 - 2 * q^5 - 10 * q^6 - 6 * q^7 - 10 * q^8 + 10 * q^9 + 2 * q^10 - 3 * q^11 + 10 * q^12 - 10 * q^13 + 6 * q^14 - 2 * q^15 + 10 * q^16 - 10 * q^17 - 10 * q^18 + 8 * q^19 - 2 * q^20 - 6 * q^21 + 3 * q^22 - 9 * q^23 - 10 * q^24 + 20 * q^25 + 10 * q^26 + 10 * q^27 - 6 * q^28 - 24 * q^29 + 2 * q^30 - 7 * q^31 - 10 * q^32 - 3 * q^33 + 10 * q^34 - 22 * q^35 + 10 * q^36 - 4 * q^37 - 8 * q^38 - 10 * q^39 + 2 * q^40 - 9 * q^41 + 6 * q^42 - 11 * q^43 - 3 * q^44 - 2 * q^45 + 9 * q^46 - 18 * q^47 + 10 * q^48 + 6 * q^49 - 20 * q^50 - 10 * q^51 - 10 * q^52 - 9 * q^53 - 10 * q^54 + q^55 + 6 * q^56 + 8 * q^57 + 24 * q^58 + 10 * q^59 - 2 * q^60 - 25 * q^61 + 7 * q^62 - 6 * q^63 + 10 * q^64 - 28 * q^65 + 3 * q^66 + 2 * q^67 - 10 * q^68 - 9 * q^69 + 22 * q^70 - 30 * q^71 - 10 * q^72 - 11 * q^73 + 4 * q^74 + 20 * q^75 + 8 * q^76 + 4 * q^77 + 10 * q^78 + 3 * q^79 - 2 * q^80 + 10 * q^81 + 9 * q^82 - q^83 - 6 * q^84 + 2 * q^85 + 11 * q^86 - 24 * q^87 + 3 * q^88 - 14 * q^89 + 2 * q^90 - 13 * q^91 - 9 * q^92 - 7 * q^93 + 18 * q^94 - 35 * q^95 - 10 * q^96 - 10 * q^97 - 6 * q^98 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more